From a pack of 9 cards numbered 1-9, three cards are drawn at random and laid on a table from left to right. What is the probability that the digits are drawn in descending order?

I know the answer is #1/6# but am unsure how to get to it.

Thanks!

1 Answer
George C.
Oct 16, 2017

#1/6#

Explanation:

The number of cards in the pack is irrelevant - they just need to be distinct numbers.

Whichever #3# cards are drawn will consist of #3# distinct numbers with exactly #1# way to order in descending order.

The total number of different possible orders of the #3# cards drawn is #3! = 3 * 2 * 1 = 6#, since there are #3# choices for the first card, #2# for the second and one for the third.

So the probability of drawing the cards in descending order is:

#1/(3!) = 1/6#

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